Estimating body volumes and surface areas of animals from cross-sections

Abstract

Background: Body mass and surface area are among the most important biological properties, but such information is lacking for some extant organisms and most extinct species. Numerous methods have been developed for body size estimation of animals for this reason. There are two main categories of mass-estimating approaches: extant-scaling approaches and volumetric-density approaches. Extant-scaling approaches determine the relationships between linear skeletal measurements and body mass using regression equations. Volumetric-density approaches, on the other hand, are all based on models. The models are of various types, including physical models, 2D images, and 3D virtual reconstructions. Once the models are constructed, their volumes are acquired using Archimedes' Principle, math formulae, or 3D software. Then densities are assigned to convert volumes to masses. The acquisition of surface area is similar to volume estimation by changing math formulae or software commands. This article presents a new 2D volumetric-density approach called the cross-sectional method (CSM).

Methods: The CSM integrates biological cross-sections to estimate volume and surface area accurately. It requires a side view or dorsal/ventral view image, a series of cross-sectional silhouettes and some measurements to perform the calculation. To evaluate the performance of the CSM, two other 2D volumetric-density approaches (Graphic Double Integration (GDI) and Paleomass) are compared with it.

Results: The CSM produces very accurate results, with average error rates around 0.20% in volume and 1.21% in area respectively. It has higher accuracy than GDI or Paleomass in estimating the volumes and areas of irregular-shaped biological structures.

Discussion: Most previous 2D volumetric-density approaches assume an elliptical or superelliptical approximation of animal cross-sections. Such an approximation does not always have good performance. The CSM processes the true profiles directly rather than approximating and can deal with any shape. It can process objects that have gradually changing cross-sections. This study also suggests that more attention should be paid to the careful acquisition of cross-sections of animals in 2D volumetric-density approaches, otherwise serious errors may be introduced during the estimations. Combined with 2D modeling techniques, the CSM can be considered as an alternative to 3D modeling under certain conditions. It can reduce the complexity of making reconstructions while ensuring the reliability of the results.

Keywords: Accuracy; Biological cross-sections; Body mass estimation; Body silhouette; Surface area estimation; Volumetric-density approach.

Figure 1. Data collection process of the CSM.

(A) The 3D model of a humpback whale (Megaptera novaeangliae), from Gutarra et al. (2022), published under the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/). (B) Main body of the same model, with fins separated and removed. (C) Side view of the main body. (D) Side view of the main body after being sliced into 10 slabs. (E) One of the cross-sections of the main body, with the identity segment marked in red.

Figure 2. Illustrations of a slab and subslabs.

(A) A slab equally partitioned into $n$ subslabs, with the $k$th subslab marked in blue and identity segments marked in red. (B) The $k$th subslab, with an arbitrary cross-section $B_s$ marked in green and its identity segment $d_s$.

Figure 3. 3D models used for validation.

(A) Humpback whale (Megaptera novaeangliae). (B) Orca (Orcinus orca). (C) Harbor porpoise (Phocoena phocoena). (D) Bottlenose dolphin (Tursiops truncatus). (E) Southern right whale (Eubalaena australis). (F) Liopleurodon. (G) Thalassomedon. (H) Ophthalmosaurus. (I) Temnodontosaurus. (J) Atlantic sturgeon (Acipenser oxyrhynchus oxyrhynchus). (K) Hawksbill sea turtle (Eretmochelys imbricata). (L) Manta ray (Mobula cf. birostris). Image source: (A, B, F, G) are 3D models from Gutarra et al. (2022), and (H and I) are from Gutarra et al. (2019), all published under the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0). Other models are from https://sketchfab.com/DigitalLife3D, published under the CC BY-NC 4.0 license (https://creativecommons.org/licenses/by-nc/4.0/).

Figure 4. Representative cross-sections of the animal models.

(A) Humpback whale (Megaptera novaeangliae). (B) Orca (Orcinus orca). (C) Liopleurodon. (D) Ophthalmosaurus. (E) Atlantic sturgeon (Acipenser oxyrhynchus oxyrhynchus). (F) Hawksbill sea turtle (Eretmochelys imbricata). Sizes of cross-sections not to scale. 3D models (A–C) are from Gutarra et al. (2022), and (D) is from Gutarra et al. (2019). (E and F) are from https://sketchfab.com/DigitalLife3D.

Figure 5. The bottlenose dolphin selected as a working example.

Main body of the dolphin, with identity segments (red) and 12 representative cross-sections (blue).

Figure 6. Reconstruction of Tyrannosaurus rex AMNH 5027.

(A) Skeletal reconstruction and body cross-sections. (B) Main body of AMNH 5027 partitioned into eight slabs by the seven cross-sections (red). The anterior base of the fifth slab is represented by the red dashed line, which almost overlaps the vertical plane containing the CM. The posture of hindlimb was adjusted for soft tissue reconstruction. The cross-section of hindlimb (green) was reconstructed following Paul (1988).

Figure 7. Results of the first test.

Each model tested was treated as one slab and partitioned into 2–16 subslabs.

Figure 8. Results of the second test.

Every model tested was sliced into 2–16 slabs, each of which was further divided into 10 subslabs.